Contents

Abstract

This example shows how to run an atomistic simulation of fracture of an iron symmetric tilt grain boundary. A parallel molecular dynamics code, LAMMPS[1], is used to calculate stresses at the grain boundary as the strain of the bicrystal is incrementally increased. Matlab is used to plot a stress-strain curve, and Atomeye is used to visualize the simulation.

Input

Description of Simulation

This molecular dynamics simulation calculates the stress-strain relationship of an iron symmetric tilt grain boundary under fracture. The grain boundary structure used in this example is a <100> Σ5(210) symmetric tilt grain boundary. The potential used to generate the structure, the Hepburn and Ackland (2008) Fe-C interatomic potential[2], is also used in this script. The simulation cell is defined such that the bicrystal is pulled in the y-direction, or perpendicular to the boundary interface, to increase strain. The strain in increased for a specified number of times in a loop, and the stress is calculated at each point before the simulation loops. The stress and strain values are output to a separate file which can be imported in a graphing application for plotting.

Grain boundary structure file

The grain boundary structure that was generated prior to this example can be found here. Store the text in "Fe_110_sig3.txt" to use it.

LAMMPS input script

This input script was run using the November 2010 version of LAMMPS. Changes in some commands in more recent versions may require revision of the input script. This script runs the simulation with a previously generated grain boundary file, which is fed to the variable "datfile." The variable "nloop" defines how many times the strain will be increased and the number of points at which the stress is calculated. Other variables, such as the strain increment and the number of replications, can be changed in the input file. To run this script, store it in "in.gb_fracture.txt" and use "lmp_exe < in.gb_fracture.txt" in a UNIX environment where "lmp_exe" refers to the LAMMPS executable.

Before strain is applied to the atoms, those atoms that are far from the grain boundary (defined by the variable deldist) are deleted to prevent unwanted transitions between periodic boundaries and to decrease simulation time. Then two smaller groups of atoms (width of groups defined by difference in variables deldist and fixdist) are fixed by setting their forces equal to zero. These same fixed groups are then incrementally strained until the grain boundary fractures.

Output

LAMMPS datafile

The following file, named "data.Fe_110_sig3.txt" should have been created in addition to the log.lammps file. This file stores strain information in the first column, stress tensor information in the second through seventh columns, and stores the total potential energy of the cell in the eight column. The simulation should have looped 100 times (as per the "nloop" variable), so there should be 100 entries (which end at a strain of 0.1) plus the initial entry of stress and strain at zero.

Post-Processing

Stress-Strain Plot

The stress-strain curve in Figure 1 can be generated using the following MATLAB script. The "exportfig" command saves the plot to a tiff file, but the plot can also be saved as a Mathcad figure once it appears. The three principle stresses are plotted: pxx in red, pyy in blue, and pzz in green. The shear stresses (not plotted) are stored in the fourth, fifth, and sixth columns of the stress variable.